SpringerLink
Log in

Multisynchronization of Delayed Fractional-Order Neural Networks via Average Impulsive Interval

  • Published:
Neural Processing Letters Aims and scope Submit manuscript

Abstract

This paper focuses on the multisynchronization problem of delayed fractional-order neural networks with parametric uncertainties. Firstly, partition space method is used to determine that each subnetwork of fractional-order neural networks has \(\prod \nolimits _{j=1}^n{\left( K_j+1 \right) }\) locally Mittag-Leffler stable periodic orbits or equilibrium points. Secondly, a universal impulsive controller is proposed to impose on each node except the last one, and all nodes eventually tend to the same state. By means of average impulsive interval method, linear matrix inequality (LMI) and some other inequality techniques, the sufficient conditions for the dynamical and static multisynchronization of whole systems are respectively given. Finally, two numerical examples are provided to illustrate the correctness of the theoretical results.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  1. Wu GC, Deng ZG, Baleanu D et al (2019) New variable-order fractional chaotic systems for fast image encryption. Chaos: Interdiscipl J Non Linear Sci 29(8):083103

    Article  MathSciNet  Google Scholar 

  2. Cohen MA, Grossberg S (1983) Absolute stability of global pattern formation and parallel memory storage by competitive neural networks. IEEE Trans Syst Man Cybern 13(5):815–826

    Article  MathSciNet  Google Scholar 

  3. Momani S, Odibat Z (2006) Analytical approach to linear fractional partial differential equations arising in fluid mechanics. Phys Lett A 355(4–5):271–279

    Article  Google Scholar 

  4. Kalogirou SA (2000) Applications of artificial neural-networks for energy systems. Appl Energy 67(1–2):17–35

    Article  Google Scholar 

  5. Xu SC, Wang XY, Ye XL (2022) A new fractional-order chaos system of Hopfield neural network and its application in image encryption. Chaos Solitons Fract 157:111889

    Article  MathSciNet  Google Scholar 

  6. Lee SH, Park MJ, Ji DH et al (2022) Stability and dissipativity criteria for neural networks with time-varying delays via an augmented zero equality approach. Neural Netw 146:141–150

    Article  Google Scholar 

  7. Hu C, Jiang HJ, Teng ZD (2010) Globally exponential stability for delayed neural networks under impulsive control. Neural Process Lett 31:105–127

    Article  Google Scholar 

  8. Sun PF, Zhao XD, Sun T et al (2020) Global stability at a limit cycle for switched multi-valued logical networks. Asian J Control 25:860–870

    MathSciNet  Google Scholar 

  9. Wan L, Wu A (2018) Multistability in Mittag-Leffler sense of fractional-order neural networks with piecewise constant arguments. Neurocomputing 286:1–10

    Article  Google Scholar 

  10. Wan LG, Wu AL (2018) Multistability in Mittag-Leffler sense of fractional-order neural networks with piecewise constant arguments. Neurocomputing 286(19):1–10

    Article  Google Scholar 

  11. Liu P, Zeng ZG, Wang J (2017) Multiple Mittag-Leffler stability of fractional-order recurrent neural networks. IEEE Trans Syst Man Cybern Syst 47(8):2279–2288

    Article  Google Scholar 

  12. Liu P, Zeng ZG, Wang J (2020) Asymptotic and finite-time cluster synchronization of coupled fractional-order neural networks with time delay. IEEE Trans Neural Netw Learn Syst 31(11):4956–4967

    Article  MathSciNet  Google Scholar 

  13. Yang QJ, Wu HQ, Cao JD (2021) Pinning exponential cluster synchronization for fractional-order complex dynamical networks with switching topology and mode-dependent impulses. Neurocomputing 428:182–194

    Article  Google Scholar 

  14. Meng X, Jiang BP, Gao CC (2022) Sliding mode projective synchronization for fractional-order coupled systems based on network without strong connectedness. Trans Inst Meas Control 44(4):775–783

    Article  Google Scholar 

  15. **ao YZ, Xu W, Li XC et al (2008) Complete synchronization of uncertain chaotic dynamical network via a simple adaptive control. Chin Phys B 17(1):80–86

    Article  Google Scholar 

  16. Aravinth N, Sakthivel R, Aouiti C et al (2021) Finite-time synchronization of hierarchical hybrid coupled neural networks with mismatched quantization. Neural Comput Appl 33:16881–16897

    Article  Google Scholar 

  17. Shao S, Liu X, Cao JD (2021) Prespecified-time synchronization of switched coupled neural networks via smooth controllers. Neural Netw 133:32–39

    Article  Google Scholar 

  18. **u RH, Zhang W, Zhou ZC (2022) Synchronization issue of coupled neural networks based on flexible impulse control. Neural Netw 149:57–65

    Article  Google Scholar 

  19. Wang YW, Yang W, **ao JW et al (2016) Impulsive multisynchronization of coupled multistable neural networks with time-varying delay. IEEE Trans Neural Netw Learn Syst 28(7):1560–1571

    Article  MathSciNet  Google Scholar 

  20. Lv XX, Li XD, Cao JD et al (2018) Dynamical and static multisynchronization of coupled multistable neural networks via impulsive control. IEEE Trans Neural Netw Learn Syst 29(12):6062–6072

    Article  MathSciNet  Google Scholar 

  21. Lu JQ, Cao JD (2011) Exponential synchronization of linearly coupled neural networks with impulsive disturbances. IEEE Trans Neural Netw 22(2):329–336

    Article  Google Scholar 

  22. Fang J, Zhang Y, Liu P et al (2021) Fixed-time output synchronization of coupled neural networks with output coupling and impulsive effects. Neural Comput Appl 33:17647–17658

    Article  Google Scholar 

  23. Yang X, Li C, Huang T et al (2017) Global Mittag-Leffler synchronization of fractional-order neural networks via impulsive control. Neural Process Lett 48(1):459–479

    Article  Google Scholar 

  24. Pan LJ, Cao JD, Al-Juboori UA et al (2019) Cluster synchronization of stochastic neural networks with delay via pinning impulsive control. Neurocomputing 366:109–117

    Article  Google Scholar 

  25. Zhang JE (2017) Multisynchronization for coupled multistable fractional-order neural networks via impulsive control. Complexity 2017:1–10

    MathSciNet  Google Scholar 

  26. Hua C, Ge C, Guan X (2015) Synchronization of chaotic Lure systems with time delays using sampled-data control. IEEE Trans Neural Netw Learn Syst 26(6):1214–1221

    Article  MathSciNet  Google Scholar 

  27. Lv H, He WL, Han QL et al (2019) Fixed-time pinning-controlled synchronization for coupled delayed neural networks with discontinuous activations. Neural Netw 116:139–149

    Article  Google Scholar 

  28. Wang J, Liang J, Zhang CT et al (2021) Event-triggered non-fragile control for uncertain positive roesser model with PDT switching mechanism. Appl Math Comput 406:126266

    MathSciNet  Google Scholar 

  29. Lgor F, Artem N, Pavel G (2022) Synchronization of multi-machine power systems under disturbances and measurement errors. Int J Adapt Control Signal Process 36(6):1272–1284

    Article  MathSciNet  Google Scholar 

  30. Lin HR, Wang CH, Chen CJ et al (2021) Neural bursting and synchronization emulated by neural networks and circuits. IEEE Trans Circuits Syst I Regul Pap 68(8):3397–3410

    Article  Google Scholar 

  31. Berry C, Komninos N (2022) Efficient optimisation framework for convolutional neural networks with secure multiparty computation. Comput Secur 117:102679

    Article  Google Scholar 

  32. Gao XY, Zhang P, Huang GH et al (2022) Financial information prediction and information sharing supervision based on trend assessment and neural network. Soft Comput 24(11):8087–8096

    Article  Google Scholar 

  33. Liu P, Zeng ZG, Wang J (2017) Multistability of recurrent neural networks with nonmonotonic activation functions and unbounded time-varying delays. IEEE Trans Neural Netw Learn Syst 29(7):3000–3010

    MathSciNet  Google Scholar 

  34. Tan M, Liu YF, Xu DS (2019) Multistability analysis of delayed quaternion-valued neural networks with nonmonotonic piecewise nonlinear activation functions. Appl Math Comput 341:229–255

    MathSciNet  Google Scholar 

  35. Hu B, Guan ZH, Chen GR et al (2019) Multistability of delayed hybrid impulsive neural networks with application to associative memories. IEEE Trans Neural Netw Learn Syst 30(5):1537–1551

    Article  MathSciNet  Google Scholar 

  36. Zhang FH, Zeng ZG (2021) Multistability of fractional-order neural networks with unbounded time-varying delays. IEEE Trans Neural Netw Learn Syst 32(1):177–187

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

This work was jointly supported in part by NSF of China (Nos. 11861060 and 11771259), NSF of Shaanxi University of Science and Technology (No. 2021BJ-17), Shaanxi Provincial Joint Laboratory of Artificial Intelligence (No. 2022JC-SYS-05), National program for the introduction of high-end foreign experts (No. G2023041032L), Innovative team project of Shaanxi Provincial Department of Education (No. 21JP013) and Shaanxi Province Natural Science basic research program key project (No. 2023-JC-ZD-02).

Author information

Author notes

  1. Xue Wang, **aoshuai Ding, Jian Li, **de Cao have contributed equally to this work.

Authors and Affiliations

  1. School of Mathematics and Data Science, Shaanxi University of Science and Technology, **’an, 710021, China

    Xue Wang, **aoshuai Ding & Jian Li

  2. School of Mathematics, Southeast University, Nan**g, 210096, China

    **de Cao

  3. Yonsei Frontier Lab, Yonsei University, Seoul, 03722, South Korea

    **de Cao

Authors
  1. Xue Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. **aoshuai Ding
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jian Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. **de Cao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jian Li.

Ethics declarations

Conflict of interest

The authors declare that there is no conflict of interest in this paper.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, X., Ding, X., Li, J. et al. Multisynchronization of Delayed Fractional-Order Neural Networks via Average Impulsive Interval. Neural Process Lett 55, 12437–12457 (2023). https://doi.org/10.1007/s11063-023-11427-6

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11063-023-11427-6

Keywords

Search

Navigation